My opinion on wrestler squad is - they are a way to train your population to minimize casualties during events, no more no less. One good strategy would consist on training one or two instructors and rotating your population until they get Master Rank or above, then releasing them into civilian life. Thay will teach them to dodge and wrestling move, earning you extra time and drastically reducing the civilian casualty number against low level threats such as kobolds or werebeasts.
As for having your actual military without weapons... I would not advise it at all. I've been wrong in the past, and wrestling is more deadly than it first appears, but even if scratches can be debilitating or even lethal in some conditions (because the game considers the nail to be the size of the finger), it is the equivalent of assaulting an enemy with a small bone knife. You can sever tendons, you can cut arteries, but you can do it better with a steel axe.
As for the wrestling stricto sensu, it recquires strengh to be effective. Your dwarves will John Cena a kobold, a lone goblin or a werebeast, but against a bigger creature that resist your keratine stillettos and will manhandle you if you try to wrestle it, your army will be eaten alive.
Another thing to consider is wrestling has relatively low lethality. It's okay in 1v1 because you can disable your opponent, put him on the ground and the fight is over when you start strangling. But when you are fighting 1 versus 10, the strategy becomes a lot less effective. Killing takes a lot of time, and every wrestling move you perform prevents you from dodging. And since you cannot block and cannot parry, and now cannot dodge, you are bound to receive nasty blows.
So in the end, to even make an unharmed squad even remotely viable, you would have to outfit it in full armor. And at that cost, why not adding just the remaining axe to get a regular squad ?